Problem: Find the distance between the point ${(8, -1)}$ and the line $\enspace {y = 5}\thinspace$. {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9}
Explanation: First, find the equation of the perpendicular line that passes through ${(8, -1)}$ Since the slope of the blue line is $0$ , the perpendicular line will have an infinite slope and therefore will be a vertical line. The equation of the vertical line that passes through ${(8, -1)}$ is $\enspace {x = 8}\thinspace$ We can see from the graph that the two lines intersect at the point ${(8, 5)}$ . Thus, the distance we're looking for is the distance between the two red points. Since their $x$ components are the same, the distance between the two points is simply the change in $y$ $|{-1} - ( {5} )| = 6$ The distance between the point ${(8, -1)}$ and the line $\enspace {y = 5}\enspace$ is $\thinspace6$.